What do you think?

gAr · 2011-03-26 20:48:54

Hi bobbym,

I could not prove this!

bobbym · 2011-03-26 22:39:34

Hi gAr;

gAr · 2011-03-26 23:00:34

Hi bobbym,

Nice one!
I was trying to prove it analytically.

bobbym · 2011-03-26 23:19:59

The guy I gave that to, he hated it. He is like A. He swears that is not enough, that it is not a proof. He feels a proof must invoke the Taylor series somewhere. I am not as certain as he is that I am right either.

gAr · 2011-03-26 23:29:56

But, isn't the generating function good enough?

bobbym · 2011-03-26 23:58:44

Hi gAr;

For me yes. For him no.

gAr · 2011-03-27 00:01:06

Hmmm, strange!

bobbym · 2011-03-27 00:05:21

I could not convince him even showing him that the two recurrences are the same and showing that all paths on a lattice, no matter what rules they are following, when counted must be an integer.

Anyway the OEIS is a valuable tool, that is the point.

gAr · 2011-03-27 00:15:39

Ok.
I too use oeis whenever I see an unfamiliar sequence, but did not try for this problem.

bobbym · 2011-03-27 00:30:52

Hi gAr;

That is good that you already know that. I use it a lot too.

gAr · 2011-03-27 00:42:06

Hi bobbym,

Yes, it's a really wonderful project.

bobbym · 2011-03-27 00:44:45

They used to distribute a book of all of them on project Gutenberg ( circa 1997 ) but since they have grown so large I do not think they will be doing that anymore.

gAr · 2011-03-27 01:00:08

Oh, I didn't know it was distributed as a book. I too think it won't be a good idea to release it as a book.

gAr · 2011-03-28 04:51:04

Hi bobbym,

Two die are thrown at once. The sample space is 2,3,4,5,6,7,8,9,10,11,12. How many times must this be done on average to get all eleven numbers?

In post #348, you had mentioned of markov chain. It requires 2^11 states, isn't it?

bobbym · 2011-03-28 04:53:59

Hi gAr;

I heard that, too. I do not know for sure because I have not thought about it much. I am pretty sure it will be very large.

gAr · 2011-03-28 04:58:48

Yes, we need to have each subset as a state. Computer may solve it, but typing is no fun!

bobbym · 2011-03-28 05:02:17

Also, you would need a matrix with over 4 million elements. You can have a sparse matrix but still in all.

The Coupon Collector Problem is still largely unsolved.

gAr · 2011-03-28 05:07:12

Ok.
Is it an important problem, does it have many applications?

bobbym · 2011-03-28 05:13:29

Hi gAr;

Yes, but I cannot think of them specifically. We try to think of probability and combinatoric problems in terms of is it a Birthday problem, an urn problem, a CCP, a block walking problem, etc. In other words most problems fall into one of those categories. The fact that some of those broad classes are not fully understood means that lots of other problems say like in computer programming are difficult to solve.

Just look at that CCP. If someone were to ask for 3 dice then the problem would be very difficult even with a CAS.

gAr · 2011-03-28 05:17:31

Oh, I see.
Interesting!

bobbym · 2011-03-28 05:22:47

Math builds, one thing on top of another. There are a lot of fragmented things in modern math. A lot of gaps. The CCP is one of them. That integral solution and my solution are a joke. Like I said just try to expand those methods for a 3 dice problem. I am going to take a break and do some household chores, see you later.

gAr · 2011-03-28 05:48:33

Hi bobbym,

Yes, it's frustrating to solve for 3 dice.
See you later.

bobbym · 2011-03-31 18:24:52

Hi gAr;

gAr wrote:

Yes, it's frustrating to solve for 3 dice.

It is like that really old joke, a guy can not lift his arm up so he goes to the doctor and says. "doctor, doctor, it hurts when I do that." Doctor says, "well, then don't do that!"

New Problem!

A poses this one. Factor this quartic using real coefficients only.

Now for the tough part, no packages. I mean no Sage, Mathematica, Maple, Mupad, Pari, Gap, Maxima, Derive, Reduce, wolfram alpha etc. In short, no blasted factor commands. I want to see work on this one. A is pleased with himself, he thinks B is locked out. He does not know that B,C, and D's numerical analysis training makes them experts on this type of problem.

B says) Got it! In less than 10 minutes!
C says) I got it too and in less than 7 minutes.
D says) Done! In less than 5 minutes.
E says) Whoosh! That is a tough one A.

How did you do? Can you explain your method to A?

gAr · 2011-03-31 19:34:51

Hi bobbym,

Yes, I'll follow the doctor's advice!
Couldnt' completely avoid the use of computer, since it involves real numbers.

bobbym · 2011-03-31 19:50:40

Hi gAr;

That is fine, very good!

Math Is Fun Forum

#776 2011-03-26 20:48:54

Re: What do you think?

#777 2011-03-26 22:39:34

Re: What do you think?

#778 2011-03-26 23:00:34

Re: What do you think?

#779 2011-03-26 23:19:59

Re: What do you think?

#780 2011-03-26 23:29:56

Re: What do you think?

#781 2011-03-26 23:58:44

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#782 2011-03-27 00:01:06

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#783 2011-03-27 00:05:21

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#784 2011-03-27 00:15:39

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#785 2011-03-27 00:30:52

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#786 2011-03-27 00:42:06

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#787 2011-03-27 00:44:45

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#788 2011-03-27 01:00:08

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#789 2011-03-28 04:51:04

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#790 2011-03-28 04:53:59

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#792 2011-03-28 05:02:17

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#793 2011-03-28 05:07:12

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#794 2011-03-28 05:13:29

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#795 2011-03-28 05:17:31

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#796 2011-03-28 05:22:47

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#797 2011-03-28 05:48:33

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#798 2011-03-31 18:24:52

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#799 2011-03-31 19:34:51

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#800 2011-03-31 19:50:40

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